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Class 12 Inverse Trigonometric Functions · Assertion Reason1 Marksassertion_reason

Class 12 Maths · Inverse Trigonometric Functions · Assertion Reason #31

Assertion: The range of f(x)=2sin⁻¹x+3π/2 for x∈[−1,1] is [π/2,5π/2]. Reason: The range of the principal arcsine is [0,π].

✅ Step-by-Step Solution

Final Answer: Option (C): A is true, but R is false.
  1. The actual arcsine range is [−π/2,π/2]; scaling by 2 and adding 3π/2 gives [π/2,5π/2]. Thus A is true and R false.

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